Learning quantum data with the quantum Earth Mover's distance

TL;DR

This paper introduces a quantum Wasserstein GAN utilizing the quantum Earth Mover's distance, which enhances stability and efficiency in quantum data learning compared to traditional metrics.

Contribution

It proposes the quantum Earth Mover's distance and a quantum Wasserstein GAN, offering a novel approach for stable and efficient quantum data learning.

Findings

qWGAN can learn diverse quantum data efficiently

Quantum EM distance improves learning stability

Resource requirements are polynomial in qubits

Abstract

Quantifying how far the output of a learning algorithm is from its target is an essential task in machine learning. However, in quantum settings, the loss landscapes of commonly used distance metrics often produce undesirable outcomes such as poor local minima and exponentially decaying gradients. To overcome these obstacles, we consider here the recently proposed quantum earth mover's (EM) or Wasserstein-1 distance as a quantum analog to the classical EM distance. We show that the quantum EM distance possesses unique properties, not found in other commonly used quantum distance metrics, that make quantum learning more stable and efficient. We propose a quantum Wasserstein generative adversarial network (qWGAN) which takes advantage of the quantum EM distance and provides an efficient means of performing learning on quantum data. We provide examples where our qWGAN is capable of learning a diverse set of quantum data with only resources polynomial in the number of qubits.